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Lecture 18

Bio2244 Lecture 18, 19, 20, 21 and 22.docx

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Department
Biology
Course
Biology 2244A/B
Professor
Angela White
Semester
Fall

Description
Lecture 18, 19, 20, 21 and 22 Correlation - Also called bivariate data - Basic concepts o Correlation – relationship between 2 variables o Use a scatter plot  X and Y represent a one of the two variables used and are plotted together o Linear correlation coefficient (r)  SAMPLE STATISTIC  Measures strength of correlation in a sample  Requirements  Sample data is random sample  Visual examination shows straight-line pattern  OUTLIERS REMOVED  Also, pairs of data must have bivariate normal distribution  For and x, y must be bell shaped and vice versa  Round to 3 decimals  If VALUE FROM TABLE LESS THAN COMPUTED r VALUE, significant linear correlation  Write as “Since r=?, its absolute value does exceed ? so we conclude that there is a significant linear correlation between x and y.  Properties  -1 <= r <= 1  Value of r doesn’t change if all values for 1 variable converted to different scale  Value of r not affected by choice of x or y  r measures strength of linear association  interpreting r  value of r^2 is proportion of variation in y explained by linear association between x and y  “We conclude that r^2 of variation in y can be explained by linear association between x and y. This implies that 1-r^2 of variation in y can be explained by factors other than x.”  Common error  Correlation DOES NOT IMPLY CAUSALITY o Lurking variable – variable that affects but is not in study  Averages inflate correlation coefficient  Property of linearity o Visually, looks like there is correlation but from data, r = 0 - Beyond the basics o Hypothesis testing  Null = there is no significant correlation  Alternate = there is significant correlation  Method 1  If absolute value of t > critical value, reject null o Otherwise, say “there is not sufficient evidence to conclude that there is a significant linear correlation” o T is test stat, critical value is from table A3  Method 2  Test stat is r, critical value is from table A6  If absolute of r > critical value, reject null o Centroid  For given (x, y), point (x-bar, y-bar) is centroid Regression - Basic concepts o Association between x (independent variable) and y-hat (dependent variable) o Requirements  Paired sample (x, y) are random sample  Scatterplot shows straight-line pattern  Outliers are removed o Notes  For each x, y must be bell-shaped  For different values of x, y-values must have same variance  For different values of x, distribution of y-values have means on straight line  Y-values INDEPEN
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